Which has more atoms: 1 kg of iron or 1 kg of aluminum? See the periodic table00lkrha *.k ty or Appendix B t0kka h*0ly.r.

Name several properties of materials that could be exploited to make a the:+ , 2pdwqyprermomete: , pwreqy+2pdr.

Which is larger, 1 C c(3v ukz+- qiu:c 6y(rc1 agab$^{\circ} $ or 1 F $^{\circ} $?

If system A is in thermal equilibrium with system B, but B is not )g6hpsr 7agzo.ewz3 ( in thermal equilibrium with system C, what can you say about the temperatures of A, B, and z(.heopr g 3ws6az7)g C?

A flat bimetallic strip consi:yun b 60aayt*sts of aluminum riveted to a strip of iron. When hean *6a0:t aybuyted, the strip will bend. Which metal will be on the outside of the curve? [Hint: See Table 13–1.] Why?

In the relation $\Delta$L = $\alpha$ $L_0$ $\Delta$T, should $L_0$ be the initial length, the final length, or does it matter? Explain.

The units for the coefficiu27ce,8djxv4 j jk f2vent of linear expansion $\alpha$ are $(C?)^{-1}$ and there is no mention of a length unit such as meters. Would the expansion coefficient change if we used feet or millimeters instead of meters? Explain.

Figure 13–27 shows a diagram of a simpl3uz*2 aeepi2sq x/-iy66ih t vccta:,e thermostat used to control a furnace (or other heating or cie avq/ uaei-tz*tc 2xs6, 3yci2:6hpooling system). The bimetallic strip consists of two strips of different metals bonded together. The electric switch is a glass vessel containing liquid mercury that conducts electricity when it can flow to touch both contact wires. Explain how this device controls the furnace and how it can be set at different temperatures.

Long steam pipes that are fixed at the ends o(-m2 p ,yxtbfdften have a section in the shape of a U. Wb2x -p,(ymdf thy?

A flat, uniform cylin kzd14/4vc.zwijf6uks qi t 2/lh8o7zder of lead floats in mercury at 0 $^{\circ} $ C. Will the lead float higher or lower when the temperature is raised? Explain.

When a cold mercury-in-glass thermometer is first placed i,)hd)ta+ : b5cd 1ys pvhi1hvmn a hot tub of water, the mercury initially descends a bit and then rises. Explas)c 1d+y p5vhm)1dvt b ,ahh:iin.

A glass container may break if one part of it is hev,.;i ntl m7/zdmhg9hated or cooled more rapidly th m ;mnz,g.v th9ih/7dlan adjacent parts. Explain.

The principal virtue of Pyrex glass is that its coefficient of linear expab).z3 qo.y zptnsion is much smaller than bpz .qzt. o)y3that for ordinary glass (Table 13–1). Explain why this gives rise to the increased heat resistance of Pyrex.

Will a grandfather clock, accurate at 9udt xymf/y asw8 83y.20 $^{\circ} $ C, run fast or slow on a hot day (30 $^{\circ} $ C)? Explain. The clock uses a pendulum supported on a long, thin brass rod.

Freezing a can of soda will cause its bottom and top to bulge so 1.wvgr cde.q u7/r4i-pj4biobadly the can will not standecdji q7bur-o 1i v.wg/pr44. up. What has happened?

When a gas is rapidly compressed (saymfj9-i/ q)jri us2-k r, by pushing down a piston), its temperature increases. When a gas expands against a piston, it cools. Explain these changes in temperature using the kinq2f9m /-u)rri jkji s-etic theory, in particular noting what happens to the momentum of molecules when they strike the moving piston.

Will the buoyant forcj6yvfzb+ d ni8 5pw;)me on an aluminum sphere submerged in water increase or decrease if the temperature is increas)6n m wzd5i j8+py;vbfed from 20 $^{\circ} $ C to 40 $^{\circ} $ C?

Explain in words how Charles’s law follows from (m6 n4a.rejx v*0rv4 x-ooe tdkinetic theory and the relation between average kinetic evad.o0r(jx 4mvro e*6xet- n4 nergy and the absolute temperature.

Explain in words how Gay-Lussac’s law follows from kinetic theorniev9ayl3h :h j o506by.

As you go higher in the Earth’s rfzk 11r:bq2fja1qi+ atmosphere, the ratio of $N_2$ molecules to $O_2$ molecules increases. Why?

Escape velocity for the Earth refers to th;gydm2i6+q;s o xw4kge minimum speed an object must have to leave the Earth and never return. The escape26;gos km;x+4dw yig q velocity for the Moon is about one-fifth what it is for the Earth due to the Moon’s smaller mass. Explain why the Moon has practically no atmosphere.

Alcohol evaporates more quickl nktif q; db-;6y2no/ly than water at room temperature. What can you inferqblkn ;6nt;2foyd- / i about the molecular properties of one relative to the other?

Explain why a hot humid day is far more uncomfortable than a hot dry dayxzbl97c: tp)niqp vrcg 8ek892 k +(jo at the same temper v)r8kj2+p:txp97o cnqe(izkb9gl c8 ature.

Is it possible to boil mvl8h ct r-6t sd2))qpwater at room temperature (20 $^{\circ} $ C) without heating it? Explain.

Consider two days when the air temperature is the same but the humidity is dir(+ ;4sgc2fpnq/fjsh fferent. Which is g4 +jrp/f(h s;ncsq 2fmore dense, the dry air or the humid air at the same T? Explain.

Explain why it is dangerous to open the radiator cap of an k jz/ccj ;q71boverheated automobile engin ;zj/7k qj1ccbe.

Why does exhaled air appear asguwnf:udofjks(6 d4 z8 ;;sk: a little white cloud in the winter (Fig. 13–28)?

  How many atoms are there in a 3.40lisf g,.eut. zr* pm8-gram copper penny?   $ \times10^{22}$ atoms of Cu

  How does the number of atoms in a 26.5-gram gold ring compare to the number ingiclbg5h9a- 1 a silver ringi l9ac15g-hgb of the same mass?$N_{Au}$ =    $N_{Ag}$

  “Room temperature” is often taken to be 68°F. What is 1ri ifj7qf+e j3 0kli:this on the Celsius scale?fq l3jir:ie7f i 10jk+   $^{\circ} $ C
(b) The temperature of the filament in a lightbulb is about 1800 $^{\circ} $ C. What is this on the Fahrenheit scale?    $^{\circ} $ F

  Among the highest and lowey(hqp h-mrf-;mqd w2 +st temperatures recorded are 136 $^{\circ} $F in the Libyan desert and -129 $^{\circ} $F in Antarctica. What are these temperatures on the Celsius scale?high =    $^{\circ} $ C
low =    $^{\circ} $ C

  (a) 15 $^{\circ} $ below zero on the Celsius scale is what Fahrenheit temperature?    $^{\circ} $ F
(b) 15 $^{\circ} $ below zero on the Fahrenheit scale is what Celsius temperature?   $^{\circ} $ C

  In an alcohol-in-glass thermometer, the alcohol cdi+rpjex l :4nu:-3ayf7 o-mxolumn has length 11.82 cm at 0.ym 7l j:3+-nx-xpida4of:ure0 $^{\circ} $ C and length 22.85 cm at 100.0 $^{\circ} $ C. What is the temperature if the column has length
(a) 16.70 cm,    $^{\circ} $ C
(b) 20.50 cm?    $^{\circ} $ C

  A concrete highway is built jaak3 n(fwe 2s4+f2xhsscc5) of slabs 12 m long (20 $^{\circ} $ C). How wide should the expansion cracks between the slabs be (at 20 $^{\circ} $ C) to prevent buckling if the range of temperature is -30 $^{\circ} $ C to +50 $^{\circ} $ C?    m

  Super Inva$^{TM}$, an alloy of iron and nickel, is a strong material with a very low coefficient of linear expansion [0.2$ \times10^{ -6}$(C?)$^{-1}$]
A 2.0-m-long tabletop made of this alloy is used for sensitive laser measurements where extremely high tolerances are required. How much will this table expand along its length if the temperature increases 5.0 $^{\circ} $ C? Compare to tabletops made of steel.   $ \times10^{-6 }$ m    $ \times10^{-4 }$ m

  The Eiffel Tower (Fig. 13–29) is- 7ytk+n mkqe3 built of wrought iron approximately 300 m tall. Estimate how much its height changes between July (average temperature of 25°C) and January (+t73 mkq -ykenaverage temperature of 2 $^{\circ} $ C). Ignore the angles of the iron beams, and treat the tower as a vertical beam.    m

  To make a secure fit, rivets that are larger than the rivet hole ar*.zkm ct ob0e9e often used and the rivet is cooled (usually in dry ice) before it is placed in the hole. A steel rivet 1.871 cm in diameter is to be placed in a hole 1.869 cm in diametzmk*t09o c .eber at 20 $^{\circ} $ C. To what temperature must the rivet be cooled if it is to fit in the hole?    $^{\circ} $ C

  The density of water ont),; b0e.igg f d5 epvq8uo+at 4 $^{\circ} $ C is $ 1\times10^{3 }kg/m^3$ What is water’s density at 94 $^{\circ} $ C?    kg/$m^3$

  A quartz sphere is 8.75 cm in diameter. What will be its change in voy7u ;0vdoodj)+dvva8gb k,k 9lume if it is heated from gkvu8a; b ko7d9)v0 ,d+ojyvd30 $^{\circ} $ C to 200 $^{\circ} $ C?    $ \times10^{ -2}cm^3$

  An ordinary glass is filled to the brim with 350.0 mL of water at 100. psdlpa*6f,, an ):mdk 7geg7p0$^{\circ} $ C. If the temperature decreased to 20.0 $^{\circ} $ C, how much water could be added to the glass?    mL

  It is observed that 55.50 mL g 7mz5m2/pjn-a3 zdx 8 kqsl;nof water at 20 $^{\circ} $ C completely fills a container to the brim. When the container and the water are heated to 60 $^{\circ} $ C, 0.35 g of water is lost. (a) What is the coefficient of volume expansion of the container?    $ \times10^{-5 }$ /$C^0$(b) What is the most likely material of the container? The density of water at 60°C is 0.98324g/ml.

  (a) A brass plug is to be pla;ko a*p*1cu rxw 3p;cyvdmt (.ced in a ring made of iron. At 20 $^{\circ} $ C, the diameter of the plug is 8.753 cm and that of the inside of the ring is 8.743 cm. They must both be brought to what common temperature in order to fit?    $^{\circ} $ C
(b) What if the plug were iron and the ring brass?    $^{\circ} $ C

If a fluid is contained in a long, narrow vessel so it can ex sam2p jk,erddo9,2+epand in essentially one direction only, show that the effective coefficient of linear expansion is approximately m,+9re,oj esd kapd22 equal to the coefficient of volume expansion $\beta$.

(a) Show that the change in the dee vmgs+- y *2joxgmk46nsity $\rho$ of a substance, when the temperature changes by $\Delta$T is given by $\rho$ = -$\beta$$\rho$$\Delta$T
(b) What is the fractional change in density of a lead sphere whose temperature decreases from 25 $^{\circ} $ C to -40 $^{\circ} $ C？

A uniform rectangular plate of t+ kr2gn)xu2llength l and width w has coefficient of linear expansix +2ut kr)2glnon $\alpha$ Show that, if we neglect very small quantities, the change in area of the plate due to a temperature change $\Delta$T is $\Delta$A = 2$\alpha l w$$\Delta$T See Fig. 13–30.

Show that for an isotropic sop*az u q 0ph-v+-lym;olid, $\beta$ = 3$\alpha$ if the amount of expansion is small. $\beta$ and $\alpha$ are the coefficients of volume and linear expansion, respectively. [Hint: Consider a cubical solid, and neglect very small quantities. See also Problem 18 and Fig. 13–30.]

  The pendulum in a grandfather clock is (xwp/o.-s,hf1a k uv)qnm+m3*vr ymt made of brass and keeps perfect time at 1- ypt,31vmukr s+./(mov)qf*anx mhw 7 $^{\circ} $ C. How much time is gained or lost in a year if the clock is kept at 25 $^{\circ} $ C? (Assume the frequency dependence on length for a simple pendulum applies.)$\approx$    min(Round to the nearest integer)

  (a) The tube of a mercury thghd0n-eln dm-qj 736uermometer has an inside diameter of 0.140 mm. The bulb has a volume of 0.25l 37 njhgnud0-6-demq5 $cm^3$ How far will the thread of mercury move when the temperature changes from 11.5 $^{\circ} $ C to 33.0 $^{\circ} $ C? Take into account expansion of the Pyrex glass.    cm(b) Determine a formula for the length of the mercury column in terms of relevant variables. Ignore tube volume compared to bulb volume.

  A 23.4-kg solid aluminum uzd25 ei b(bul/p /(ndcylindrical wheel of radius 0.41 m is rotating about its enbu(25( dp// ziuldbaxle on frictionless bearings with angular velocity $\omega$ = 32.8 rad/s If its temperature is now raised from 20.0 $^{\circ} $ C to 75.0 $^{\circ} $ C, what is the fractional change in $\omega$?   

  An aluminum bar has the desired kymk8p p3cq,t0o e0d,length when at 15°C. How much stress is required to c0k m etd yk,pqpo083,keep it at this length if the temperature increases to 35 $^{\circ} $ C?    $ \times10^{7 }$ N/$m^2$

(a) A horizontal steel I-beam of cross-sesrq2qt4p/ 9nactional area 0.041$m^2$ is rigidly connected to two vertical steel girders. If the beam was installed when the temperature was 30$^{\circ} $ C, what stress is developed in the beam when the temperature drops to -30 $^{\circ} $ C (b) Is the ultimate strength of the steel exceeded? (c) What stress is developed if the beam is concrete and has a cross-sectional area of 0.13$m^2$ Will it fracture?

  A barrel of diameter 134.122 cm at 8 0mo4vecfthebv47: q20$^{\circ} $ C is to be enclosed by an iron band. The circular band has an inside diameter of 134.110 cm at 20$^{\circ} $ C. It is 7.4 cm wide and 0.65 cm thick.
(a) To what temperature must the band be heated so that it will fit over the barrel? $\approx$   $^{\circ} $ C(Round to the nearest integer)
(b) What will be the tension in the band when it cools to 20$^{\circ} $ C?    N

  What are the following tempera(6drgcd 1 ).cvn vhnk:tures on the Kelvin scale:
(a) 86$^{\circ} $ C,    K
(b) 78$^{\circ} $F,    K
(c) -100$^{\circ} $C    K
(d) 5500°C,    K
(e) -459$^{\circ} $F    K

  Absolute zero is what temperature sk p dbo21-l+xjym:7 ofs ,6h5:ucqyy on the Fahrenheit scale?    $^{\circ} $ F

  Typical temperatures in the izixen,p0(s2swa1 ) n p,q1vljnterior of the Earth and Sun are about 4000$^{\circ} $ C and $ \times10^{6 }$ $^{\circ} $ C respectively.
(a) What are these temperatures in kelvins?    K    $ \times10^{ 6}$K
(b) What percent error is made in each case if a person forgets to change $^{\circ} $ C to K? $\approx$    %(Round to the nearest integer) $\approx$    %(Round to three decimal places)

  If 3 $m^2$ of a gas initially at STP is placed under a pressure of 3.20 atm, the temperature of the gas rises to 38.0$^{\circ} $ C. What is the volume?    $m^3$

  In an internal combustion engine, air at atmospheric pressure and a9+hvh j7+aprx temperature of v7h9ja+rxp+h about 20$^{\circ} $C is compressed in the cylinder by a piston to $\frac{1}{9}$ of its original volume (compression ratio = 9.0). Estimate the temperature of the compressed air, assuming the pressure reaches 40 atm.    $^{\circ} $ C

  Calculate the density of oxygen at STP using the ideal-842erkc)5v9f5q cb ypyrhqj gas law.    kg/$m^3$

  A storage tank contains jgnmswe;cu : knm. ;+;21.6 kg of nitrogen ($N_2$) at an absolute pressure of 3.65 atm. What will the pressure be if the nitrogen is replaced by an equal mass of $CO_2$    atm

  A storage tank at STP contains 18.5 kg of nitro6q-h /-n +n2lecwhvdbgen ($N_2$)
(a) What is the volume of the tank? $\approx$   $m^3$(“Round to one decimal places)
(b) What is the pressure if an additional 15.0 kg of nitrogen is added without changing the temperature?    $ \times10^{5 }$Pa    atm

  If 18.75 mol of helium gas ;3a, othnc7ei is at 10.0$^{\circ} $C and a gauge pressure of 0.350 atm, (a) calculate the volume of the helium gas under these conditions.    $m^3$
(b) Calculate the temperature if the gas is compressed to precisely half the volume at a gauge pressure of 1.00 atm.    $^{\circ} $ C

  What is the pressure inside a 35.0-L contaxk +gv+iizo/el827 lviner holding 105.0 kg of argon gas at 385 Kvi e7+zkv glxl /+i28o?   $ \times10^{ 8}$Pa

  A tank contains 26.0 4eyd3mkzd a*p . a;a3ykg of $O_2$ gas at a gauge pressure of 8.70 atm. If the oxygen is replaced by helium, how many kilograms of the latter will be needed to produce a gauge pressure of 7.00 atm?    kg He

  A hot-air balloon achieves its buoyant lift by heatih5e240t sp ndnrn c,1dng the air inside the balloon, which makes it less dense than the air oucens5p24dt d1 0,nhrntside. Suppose the volume of a balloon is 1800 $m^3$ and the required lift is 2700 N (rough estimate of the weight of the equipment and passenger). Calculate the temperature of the air inside the balloon which will produce the required lift. Assume that the outside air temperature is 0 $^{\circ} $ C and that air is an ideal gas under these conditions. What factors limit the maximum altitude attainable by this method for a given load? (Neglect variables like wind.) $\approx$    $^{\circ} $ C(Round to the nearest integer)

  A tire is filled with air at 1x woq7yn5a7pyg013 4ep9 rnns(mfdi 05 $^{\circ} $ C to a gauge pressure of 220 kPa. If the tire reaches a temperature of 38 $^{\circ} $ C, what fraction of the original air must be removed if the original pressure of 220 kPa is to be maintained?    %

  If 61.5 L of oxygen at 1t2n9 y;(e.i(.fewww-nk f bmk8.0 $^{\circ} $ C and an absolute pressure of 2.45 atm are compressed to 48.8 L and at the same time the temperature is raised to 50.0°C, what will the new pressure be?    atm

  A helium-filled balloon escapes a child’s hand at sea leve9)k adkzjc7;t vch2eys2 cl 25l and 20.0 $^{\circ} $ C. When it reaches an altitude of 3000 m, where the temperature is 5.0 $^{\circ} $ C and the pressure is only 0.70 atm, how will its volume compare to that at sea level?    times the original volume

  Calculate the number of molecu sok*vqmj/p)+ 0 hyq8lles / $m^3$ in an ideal gas at STP.    $ \times10^{25 }$ molecules /$m^3$

  How many moles of water are there in 1.000 Laviygi x;7o/aq 9r6 0qvn8va. ? How many molecules?    mol    $ \times10^{25 }$ molecules

  Estimate the number of (a) moleaie98n d(pl4p s,    $ \times10^{22 }$ moles and (b) molecules of water in all the Earth’s oceans. Assume water covers 75% of the Earth to an average depth of 3 km. $\approx$    $ \times10^{46 }$ molecules

  A cubic box of volume s/t dmksl3*.1 ix ieu5+ kee1n5.1$ \times10^{ -2}m^3$ is filled with air at atmospheric pressure at 20 $^{\circ} $ C. The box is closed and heated to 180 $^{\circ} $ C. What is the net force on each side of the box?    N

  Estimate how many molecules of air are in eac.q ;n(i 4l 2lclcdkxd/h 2.0-L breath you inhale that were aqdkl.dx 24/lc(i;l cnlso in the last breath Galileo took. [Hint: Assume the atmosphere is about 10 km high and of constant density.]   $\frac{molecules}{breath}$

  (a) What is the average translational kinetic energy of an oxygen molecule , mj ado0gm-:r jmw+v5at STj + g w0mrja:vmd-om5,P?    $ \times10^{-21 }$ J
(b) What is the total translational kinetic energy of 2.0 mol of $O_2$ molecules at 20 $^{\circ} $ C?   $ \times10^{3 }$ J

  Calculate the rms speed of helium atoms near the surface of the Sun at a temperaop cr30zv2g:3pnyz 7e4i+q rst7yp3q+2z r3 c40 srvn:e gopizure of about 6000 K.    m/s

  By what factor will the rms speed of gas molec8xs(9t 8ii gdbmjs-3x ules increase if the temperature is increased fr8s ti gs-(9dixm8 bjx3om 0 $^{\circ} $ C to 100 $^{\circ} $ C?   

  A gas is at 20 $^{\circ} $ C. To what temperature must it be raised to double the rms speed of its molecules?    $^{\circ} $ C

  Twelve molecules have tt:nmdc-*gmdr:a 2e)cl6q3 yv he following speeds, given in units of km/s: 6, 2, 4, 6, 0, 4, 1, evc3rd6:td a-g*ln:m)my c 2q 8, 5, 3, 7, and 8. Calculate the rms speed. $v_{rms}$ =    km/s

  The rms speed of molesekc.rp;c i1 mgn) 4 jn).p9oocules in a gas at 20.0 $^{\circ} $ C is to be increased by 1.0%. To what temperature must it be raised?    $^{\circ} $ C

  If the pressure of a gas is doubled while its volume is held constant, by9f0q .k m-sqz93dd6q f:otpdg what factomfftsp6k. 0dd:9 3 q qozdg-9qr does $v_{rms}$ change?   

Show that the rms speed of molecules inwe bjqal 7i pl .r8chn-*pl (e-7ku-v. a gas is given by $v_{rms}$ = $\sqrt{3P\\rho}$ where P is the pressure in the gas, and $\rho$ is the gas density.

Show that for a mixture of two gases atd*y(0d 5ng c9wfi: kdow(z2kt the same temperature, the ratio of their r:d(*yk z gdwnkdo 9i w0c2ft(5ms speeds is equal to the inverse ratio of the square roots of their molecular masses.

  What is the rms speed of nitrogen molecules contained in an 8.5d t5*4-n4qksxpf ,zjtex o6 2e$-m^3$ volume at 2.1 atm if the total amount of nitrogen is 1300 mol?    m/s

  Calculate (a) the rms speed of an oxygen molz hd n32 5 (iqmupke;-q0v9sh,5smpk ucsih/2ecule at 0 $^{\circ} $ C    m/s
(b) determine how many times per second it would move back and forth across a 7.0-m-long room on the average, assuming it made very few collisions with other molecules.    round trips per sec

  What is the average distance between nitrogen moleculr xw.suq+9vm yims)o+26c ej4es at STP?    $ \times10^{-9 }$m

  (a) Estimate the rms speed of an amino acid whose molecular mass is 89 u in /ygi 1vde y1,n3 r0nlxa living cell at 37 1ly nye3dxv/ rg ,01ni$^{\circ} $ C.    m/s
(b) What would be the rms speed of a protein of molecular mass 50,000 u at 37 $^{\circ} $ C?    m/s

Show that the pressure P of a gas can be written Pi4rm8vr a 3v28:r2p4zi s zxty = $\frac(1)(3)\rho v^2$ where $\rho$ is the density of the gas and v is the rms speed of the molecules.

  The two isotopes of ura,ueq7,x 8e honhh9v l2nium, $^{235}$U and $^{238}$U (the superscripts refer to their atomic mass), can be separated by a gas-diffusion process by combining them with fluorine to make the gaseous compound UF$_6$ Calculate the ratio of the rms speeds of these molecules for the two isotopes, at constant T.   

(a) At atmospheric pressure, in what phases ca5a7c7qfbl,t0c fe;i rn $CO_2$ exist? (b) For what range of pressures and temperatures can $CO_2$ be a liquid? Refer to Fig. 13–21.

Water is in which phase when the pressutpzmxo0 yfh( 0m0d4 *gien 1r;re is 0.01 atm and the temperature is (a) 90mh nx* toe0z0 m04;r1igfp dy( $^{\circ} $ C, (b) -20 $^{\circ} $ C.

  What is the dew point (approximatqt9d b,g.q8-exwh om3ely) if the humidity is 50% on a day when the temperature 9-bqhtwd g.q 38xem,o is 25 $^{\circ} $ C?$\approx$    $^{\circ} $ C(Round to the nearest integer)

  What is the air pressure at a place where waczb57 j0x1otlter boils at 90 $^{\circ} $ C?    torr    Pa    atm

  If the air pressure at a particular plw+xsp5jd1 5tl ace in the mountains is 0.72 atm, estimate the temperature 5wjdtl5 +pxs1 at which water boils. $\approx$ =    $^{\circ} $ C

  What is the temperature on a day when c7r7v x l9 )cp81dcwztthe partial pressure of water is 530 Pa and the relativp7zcc87t9)lvcxrd1 w e humidity is 40%? $\approx$ =    $^{\circ} $ C(Round to the nearest integer)

  What is the partial pressure of water on a day when theomk l;*z- .:dj*(7jawgkgpad temperature is 25 $^{\circ} $ C and the relative humidity is 35%?    Pa

  What is the approximate pressure inside atwxo8(wvz q nb cued+e+o( /( c9m1zx7 pressure cooker if the water is boiling at a t+u9+owv(b n(w8e 1m7zxx c(ezqd /oc temperature of 120 $^{\circ} $ C? Assume no air escaped during the heating process, which started at 20 $^{\circ} $ C.    atm

  If the humidity in a rij 9.fn7n;5sc,ou jmn0 oxyo 3oom of volume 680$m^3$ at 25 $^{\circ} $ C is 80%, what mass of water can still evaporate from an open pan?    kg

  Air that is at its dew pointuh5) qtra 7mi- of 5 $^{\circ} $ C is drawn into a building where it is heated to 25. What will be the relative humidity at this temperature? Assume constant pressure of 1.0 atm. Take into account the expansion of the air.    %

  Estimate the time needed for a glyciu ,ctq( 6b(ztune molecule (see Table 13–4) to diffuse a distance of 15(u (qztc,6 utb $\mu m$ in water at 20$^{\circ} $ C if its concentration varies over that distance from 1 mol/$m^3$ to 0.4 mol/$m^3$ Compare this “speed” to its rms (thermal) speed. The molecular mass of glycine is about 75 u. t $\approx$    s ([color=rgba(0, 0, 0, 0.85)]Round to one decimal places) $v_{diffuse}$    $ \times10^{ -5}$ m/s
$v_{rms}$    m/s

  Oxygen diffuses from the surface of insects to the interi(b4u6jb,wm+*f trdt sor through tiny tubes called tracheae.b t4dj6wt u sm,*br+f( An average trachea is about 2 mm long and has cross-sectional area of $ 2\times10^{-9 } m^2$ Assuming the concentration of oxygen inside is half what it is outside in the atmosphere,
(a) show that the concentration of oxygen in the air (assume 21% is oxygen) at 20$^{\circ} $ C is about 8.7 mol/$m^3$ then $\approx$    mol/$m^3$(Round to one decimal places)
(b) calculate the diffusion rate J,    $ \times10^{-11 }$ mol/s
(c) estimate the average time for a molecule to diffuse in. Assume the diffusion constant is $ 1\times10^{-5 } m^2/s$    s

  A precise steel tape8xx g8on(3omqc hkd e+;bh (vc+q j5m- measure has been calibrated at 20$^{\circ} $C. At 34$^{\circ} $C,
(a) will it read high or low,
(b) what will be the percentage error?    $ \times10^{-4 }$ %

  A precise steel tape measure has b- kcso 5gf5k:cs rc2g1een calibrated at 20$^{\circ} $C. At 34$^{\circ} $C,
(a) will it read high or low,
(b) what will be the percentage error?    $ \times10^{-4 }$ %

  A Pyrex measuring cup was calibrat 3ahp 2a 5edna,e-7r7xzb4*g( w dxypled at normal room temperature. How much error will be made in a recipe calling for 300 mL of cool wag-p47n, hdrx2p eawx y el dzaa3b(*57ter, if the water and the cup are hot, at 80$^{\circ} $C, instead of at 20$^{\circ} $C? Neglect the glass expansion.$\approx$    ml

  The gauge pressure in a helium gas cylinder is initially 28 a; ht ea+8rs6uig0is /ttm. After many balloons have been blown up, the gauge pressure has decreased to 5 atm. What fraction of the original gas remaii6+t ih8/sa ;g rs0etuns in the cylinder?   

  Estimate the number of airph j, 2ddib/-w molecules in a room of length 6.5 m, width 3.1 m, and height 2.5 m. Assume the temp-phi,jw db2d/ erature is 22$^{\circ} $C. How many moles does that correspond to?    $\times10^{27 }$ molecules    moles

  In outer space the density of matter is about one 2ck tc1aim2bwq2 g: 8ratom per $cm^3$ mainly hydrogen atoms, and the temperature is about 2.7 K. Calculate the rms speed of these hydrogen atoms, and the pressure (in atmospheres).$v_{rms}$ =    m/s    $ \times10^{-22 }$ atm

  The lowest pressure attainable using the best available vacuupb3eimav 5*e 2i rx3w4m techniques is aboxv43*a3 mibe 2w r5epiut $10^{-12} N/m^2$ At such a pressure, how many molecules are there per $cm^3$ at 0$^{\circ} $C?    $\frac{molecules}{cm^3}$

  If a scuba diver fills his lungs to full capacity of 5.5 L when 10 m 1 ld+3r f t0gferkn3dvif4j 32below the surface, to what volume would his l nflegrvf+t3 rk2d3dif43 0j1ungs expand if he quickly rose to the surface? Is this advisable?    L

  A space vehicle returning froaud4l(gj9q; ei/htt7 m the Moon enters Earth’s atmosphere at a speed of about 40,000 km/h Molecules (assume nitrogen) striking the nose of the vehicle with this speed correspond to what temperature? (Because of this high temperature, t ual4;t9q( h7gde/ijthe nose of a space vehicle must be made of special materials; indeed, part of it does vaporize, and this is seen as a bright blaze upon reentry.)    K

  The temperature of an ideal gas ihxrw join*)tk0a 8n5 gkz-*3 ys increased from 110$^{\circ} $C to 360$^{\circ} $C while the volume and the number of moles stay constant. By what factor does the pressure change? By what factor does $v_{rms}$ change?$\frac{P_2}{P_1}$ =    $\frac{(v_{rms})_2}{(v_{rms})_1}$ =   

  A house has a volumexo*c t5qhik5 (1wa nt8 of 770m$^2$ (a) What is the total mass of air inside the house at 20$^{\circ} $C?    kg
(b) If the temperature drops to -10$^{\circ} $C what mass of air enters or leaves the house?    kg

  From the known value of atmospheric pressure at the surface gcr.gv cj du.1 *dq)ey8 f8 g,rs,cwh5of the Earth, estimate the total number of air molecus5c. ),cur g1vgcf 88,w eydj *dgr.qhles in the Earth’s atmosphere.    $ \times10^{44 }$ molecules

  What is the rms speegbi4wi/u*l; n d of nitrogen molecules contained in a 7.6$-m^3$ volume at 4.2 atm if the total amount of nitrogen is 1800 mol?    m/s

  A standard cylinder of oxygen used infwd7 gttvf+x. oyg9a5 *07o rr a hospital has gauge pressure = 2000 psi (13,800 kPa) and at T = 259K How long will the cylinder last if the flow rate, meas.+fxtao7 g 75wv0d fgtro*y9rured at atmospheric pressure, is constant at 2.4 L/min. $\approx$    hour

  An iron cube floats ij/htpi + or-n:9o.hedn a bowl of liquid mercury at 0$^{\circ} $C. (a) If the temperature is raised to 25$^{\circ} $C, will the cube float higher or lower in the mercury? ----待选择----lowerheigher 
(b) By what percent will the fraction of volume submerged change?    %

  The density of gasoline at tbh4vvpz/ +i80$^{\circ} $C is 0.68$ \times10^{3 }kg/m^3$ What is the density on a hot day, when the temperature is 38$^{\circ} $C?    kg/$m^3$
What is the percentage change?    %

  If a steel band were to fit snuglnd*+ won5g cn.y around the Earth’s equator at 25$^{\circ} $C, but then was heated to 45$^{\circ} $C, how high above the Earth would the band be (assume equal everywhere)?    m

  A brass lid screws tightly og qe8ey 3zz1*z/e, jvmnto a glass jar at 20$^{\circ} $C. To help open the jar, it can be placed into a bath of hot water. After this treatment, the temperatures of the lid and the jar are both 60$^{\circ} $C. The inside diameter of the lid is 8.0 cm at 20$^{\circ} $C. Find the size of the gap (difference in radius) that develops by this procedure.    cm

  The first length standard,d: ;t ezn5ur(ltuz,t: adopted in the 18$^{th}$ century, was a platinum bar with two very fine marks separated by what was defined to be exactly 1 m. If this standard bar was to be accurate to within $\pm1.0 \mu m$ how carefully would the trustees have needed to control the temperature? The coefficient of linear expansion for platinum is $ 9\times10^{ -6}C/^{-1}$. $\pm$ =    C$^{\circ} $

  A scuba tank, when fully charged, has a pressure of 195 ambp4p qabb8wgaj:()yb1a(+ wtm at 20$^{\circ} $C. The volume of the tank is 11.3 L.
(a) What would the volume of the air be at 1.00 atm and at the same temperature?    L
(b) Before entering the water, a person consumes 2.0 L of air in each breath, and breathes 12 times a minute. At this rate, how long would the tank last?    min
(c) At a depth of 20.0 m of sea water and temperature of 10$^{\circ} $C, how long would the same tank last assuming the breathing rate does not change?    min

  The escape speed from thegirg b 31vxkgu5vy/*+ Earth is $ 1.12\times10^{4 } m/s$ so a gas molecule travelling away from Earth near the outer boundary of the Earth’s atmosphere would, at this speed, be able to escape from the Earth’s gravitational field. At what temperature is the average speed of
(a) oxygen molecules,    $ \times10^{5 }$K
(b) helium atoms equal to $ 1.12\times10^{4 } m/s$    $ \times10^{4}$K
(c) Can you see why our atmosphere contains oxygen but not helium?

  A 1.0-kg trash-can lid is suspendedvvk25qj01 *:dz dfw *5zk xdnxs2nb* d against gravity by tennis balls thrown verticad:*n vqb z2x*5sxdd jw1k2 d0fv5kzn *lly upward at it. How many tennis balls per second must rebound from the lid elastically, assuming they have a mass of 0.060 kg and are thrown at 12m/s   balls/s

  A scuba diver releases a 3.00-cm-diameter (spherical) bubbl q2up vz-s*yi v5oh /o.w;tvq7e of air from a depth of 14.0 m in a lake. Assume the temperature is cons2*yo/v;5 izpuqs7- oqt.v hw vtant at 298 K, and the air behaves as a perfect gas. How large is the bubble when it reaches the surface?    cm

  Calculate the total water vapor pressure in the air (gkyjn2yy t(u b.:.scon the following two days: y:y.j g( cs2bytk(.nu
(a) a hot summer day, with the temperature 30$^{\circ} $C and the relative humidity at 40%;    Pa
(b) a cold winter day, with the temperature 5$^{\circ} $C and the relative humidity at 80%.    Pa

  A sauna has 7$m^3$ of air volume, and the temperature is 90$^{\circ} $C. The air is perfectly dry. How much water (in kg) should be evaporated if we want to increase the relative humidity from 0% to 10%? (See Table 13–3.)    kg

  Estimate the percent difference in t y aoh/p)(v;ajhe density of iron at STP, and when it is a solido (; )hajayv/p deep in the Earth where the temperature is 2000$^{\circ} $C and under 5000 atm of pressure. Assume the bulk modulus (90$\times 10^9N/m^2$) and the coefficient of volume expansion do not vary with temperature and are the same as at STP.    %  ----待选择----decreaseincrease 

(a) Use the ideal gas law to show that, for an ideal gas at constant pressure*1aopr;g agl.i k1)gp , the coefficient of v11ipr .ag)o plga*kg;olume expansion is equal to $\beta$ = 1/T where T is the temperature in kelvins. Compare to Table 13–1 for gases at T = 293K (b) Show that the bulk modulus (Section 9–5) for an ideal gas held at constant temperature is B = P where P is the pressure.

  In humid climates, people constantly dehumidify their cellars to prevent y7onwpk3po ,- rot and mildew. If the cel ok-w7,ppn y3olar in a house (kept at 20$^{\circ} $C) has 95 $m^2$ of floor space and a ceiling height of 2.8 m, what is the mass of water that must be removed from it to drop the humidity from 95% to a more reasonable 30%?    kg